Wartime show tunes set the mood, before Sheridan Smith bounds on with a spotlight lighting her from behind and making her blonde locks glow like a halo. Her big hair, wiggly walk, red dress and lipstick ooze an old-fashioned, Marilyn Monroe sort of glamour. Only the tattoos creeping down each arm suggest that we are in 2018, but then that’s Smith all over. As one of the UK’s most accomplished actors, she is equally at home playing comic period characters such as Fanny Brice in Funny Girl or a council estate rough diamond in hard-hitting Shannon Matthews kidnap drama The Moorside.

This two-hour show of orchestrated covers, laughs and introductory stories, though, is something else – and she admits to being nervous. “Usually, I play a role,” she explains, “but this is as if I’m naked. I promise not to take my clothes off … well, maybe in the second half.”

She doesn’t, but there is plenty else on offer as she rattles from big, brassy, Shirley Bassey-type numbers (Big Spender, I Smell a Rat) to bump’n’grind send ups (Addicted to Love; Superstar) and F-bomb-strewn banter. She says her water “is vodka really”, emits a loud burp (“sorry Mum!”), and turns the simple act of getting up on a high stool while wearing a tight dress into riotous, racy slapstick.

She has had a tough time lately, and public struggles following her father’s death from cancer. “I’ve been crazy for a couple of years. You might have read about it,” she admits after a boisterous version of Gnarls Barkley’s Crazy makes being of unsound mind sound a hoot. But her spectral take on Rufus Wainwright’s Dinner at Eight is exactly as she introduces it: “A beautiful song about family.”

In the second half, she strides on in a feather boa that makes her look like a giant bird, talks cheekily about “my Fanny” (referring to Brice) and introduces “Anyone ’oo Ever ’ad a ’Art by Burt Backer-crack”. Cilla Black – who sang the Bacharach song in the 1960s – was another of Smith’s great acting roles, and she reprises the voice uncannily, before donning rubber boobs for Dolly Parton’s 9 to 5 and ends Piece of My Heart by passing the mic to a bloke in the audience called Tommy, from Macclesfield.

There is always a suspicion that all of this Carry On Sheridan is her way of healing, and gradually the wounds reopen. She dedicates a lovely version of Crystal Gayle’s Talking in Your Sleep to her mum in row L, and as she profusely thanks everyone for supporting her after her “shit time”, Tommy from Macclesfield is on hand again with a tissue, to wipe away her tears.

It’s a testament to Smith’s artistic skills that she manages to sing the Dreamgirls torch song And I Am Telling You I’m Not Going despite quietly sobbing her way through it, but she recovers to turn This Is Me (“this is brave, this is bruised …”) from The Greatest Showman into a showstopping, audience arms-waving epic of determination.

A segue from I Will Survive into Happy may have over-egged the emotional pudding, but the show careers between sublime and ridiculous with giddy gusto. Somewhere amid the chaos, brass, cheeky winks, knickers jokes and spine-tingling real hurt, is a glimpse into the demanding nature of Smith’s voracious talent: she gives everything of herself to everything she does.

• Sheridan Smith is at Winter Gardens, Blackpool, 17 April. Tickets: 0844-856 1111. Then touring until 26 April.